Pith Number

pith:VMWDPYNW

pith:2011:VMWDPYNWTBOZKSLRYDFA3DKZFG

not attested not anchored not stored refs pending

Fractional calculus of variations for a combined Caputo derivative

Agnieszka B. Malinowska, Delfim F. M. Torres

arxiv:1109.4664 v1 · 2011-09-21 · math.OC · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMWDPYNWTBOZKSLRYDFA3DKZFG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:12:33.212712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab2c37e1b6985d954971c0ca0d8d59299bcbae61c52da4b4da82b11bdb59821c

Aliases

arxiv: 1109.4664 · arxiv_version: 1109.4664v1 · doi: 10.48550/arxiv.1109.4664 · pith_short_12: VMWDPYNWTBOZ · pith_short_16: VMWDPYNWTBOZKSLR · pith_short_8: VMWDPYNW

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VMWDPYNWTBOZKSLRYDFA3DKZFG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ab2c37e1b6985d954971c0ca0d8d59299bcbae61c52da4b4da82b11bdb59821c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a182f575d4de247c388ab8cef5f7500f3b39c109eb4030ec74744e808556c66b",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-09-21T22:15:28Z",
    "title_canon_sha256": "171af823dd1a03d0ff58a709a962d640d98296be58342b1bd03592dc9f5e03d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4664",
    "kind": "arxiv",
    "version": 1
  }
}